We collected a sample of 10 nearby galaxies made of 2 dwarfs and 8 spirals.
For each galaxy, we measured the distribution and kinematics of the atomic and the molecular gas from 21-cm and CO(2–1) emission line datacubes using the software \(^{\text{\textsc {3D}}}\)Barolo [1]}, which performs a tilted-ring model fitting on the observations.
Then, we calculated the radial profile of \(E_\mathrm {obs}\)  for both the gas phases.
We derived \(\tau _\mathrm {diss}\)  using the gas scale heights based on the VHE.
To this task, we used the Python tool Galpynamics [2]}.
We adopted a simple model for the kinetic energy density per unit area (\(E_\mathrm {mod}\) ) that includes the gas thermal energy and the turbulent energy expected from SNe.
This latter depends on \(\tau _\mathrm {diss}\)  and the free parameter \(\eta \) , which we assumed to be constant across the disc.
For the atomic gas, we explored two single-phase cases (assuming either cold or warm neutral medium), and the more realistic scenario of a two-phase gas.
We fitted \(E_\mathrm {obs}\)  with \(E_\mathrm {mod}\)  to find \(\eta \) .
The right panel in Fig. REF  shows the example of the atomic gas in NGC 2403 assuming a single-phase, cold neutral gas.
This case requires the maximum SN energy, as the gas thermal energy is essentially negligible.
Nonetheless, \(E_\mathrm {obs}\)  is very well reproduced by our model, notably with very low efficiency.
We find the same results for all the galaxies and for both the atomic gas and the molecular gas, which is remarkable considering that we assumed \(\eta \)  to be independent from the galactocentric radius.
Considering the galaxy sample as a whole and the systematic uncertainties (e.g. on gas temperature and \(\Sigma _\mathrm {SFR}\) ), we obtained \(\eta = 0.02^{+0.02}_{-0.01}\)  for the atomic gas and \(\eta = 0.003^{+0.007}_{-0.002}\)  for the molecular gas.
